# A game between an individual and a population: rationale

2012年4月23日追记：昆明动物所王瑞武老师基于榕小蜂的一系列研究，已经包含了这个思路。参见这两篇论文Wang et al. 2009 (doi:10.1371/journal.pone.0007802)， Wang et al. 2011 (doi: 10.1098/​rsif.2011.0063)。 看来我还得思考得再远一些，才能写出点东西。

At the first glance, the idea proposed in the last post may seem nothing new if we only consider the residents as the only players of the game. However, we are considering not only the residents but also the government as the opposite player. The overall game here can thus be classified as an Asymmetric Two-players' Game which is played Repeatedly. However, at least one of the two players is actually a population, in which each individual makes choices NOT based on the population benefit, but their own individual benefits. When a single government and its strategy is fixed, the scenario is exactly the same as the traditional multiple players' Prisoners' Dilemma or the Boxed Pigs' Game, where the Tragedy of the Commons is expected to be the outcome under certain assumptions.

Now let's look at what happens if there are a plural of governments who are in competition with one another in accumulating their own wealth. The governments who choose the 'conscience' strategy may have a disadvantage at the beginning if only a small part of its residents would resist, because it will lose more money to its residents than other governments who choose to be 'selfish'. However, when generations of the residents passed under such a government, leaving only the obedient residents left because the resistant ones are eliminated naturally, the government will be paying nothing to the residents simply because nobody will claim their money back. In contrast, under a 'selfish' government, the obidient residents will be eliminated after a plural of generations with all the left residents becoming resistent, as the result the government will finally lose the money to its residents's pockets. Finally we see that the selfish governments lose the game and the non-selfish governments win. Notice here that the time span of a generation of the residents must be shorter than that of the governments, which is the prerequisite of the outcome here. This process was introduced briefly in my last post, and in this paragraph with more details.

This government-resident model looks perfectly applicable to the interaction between cells and the mitochondia inside them. The mitochondria are the 'residents' living within a cell, the rest part of which is their 'government'. The money is embodied in ATPs, which are allocated between the mitochondria and the rest part (hereafter I will just use 'the cell' for the rest part of it). This allocation, which is actually through a biochemical mechanism, can be seen as the game being played between the mitochondrial genome and the nuclear genome during the macro-scale history of evolution. We know that indeed mitochondria replicate faster than the cell containing them get divided, which is the key prerequisite of the gaming process talked in the above paragraph. Also we know that mitochondria don't 'migrate' between cells in the natural world, which keeps the gaming process simpler than the realistic political issues. Bearing these in mind, we can then go on to talk about how nuclear and mitochondrial genomes (and/or 'epi-genomes') play games in ATPs allocation, and what outcomes are achieved under various conditions (healthy and pathological).

To be continued.

https://blog.sciencenet.cn/blog-351781-537775.html

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